«Στον καιρό μας βγήκανε πολλές νέες θρησκείες. Μια απ’ αυτές είναι κι ο τουρισμός, που τον γέννησε η κούφια και χασομέρικη περιέργεια του ανθρώπου που θέλει να σκαλίζει και να μαθαίνει χωρίς να δίνει καμμιά σημασία σ᾿ εκείνο που βλέπει κι ακούει. Οι περισσότεροι τουρίστες βαριούνται τη ζωή τους και θέλουνε να περάσουνε την ώρα […]

Here are some previous informal notes I’ve taken on the paper titled “Diffusion Maps and Coarse Graining: A Unified Framework for Dimensionality Reduction, Graph Partitioning, and Data Set Parameterization” authored by Stephane Lafon and Ann B. Lee. In this discussion, I will explore a core concept from the paper: the concept of “diffusion distance.”...

In numerous contexts of our lives, specific dyadic interactions are characterized as “negative,” a term I use advisedly given its imprecise definition. To illustrate, consider one’s ego-centric networks, which are essentially the subgraphs formed by oneself and one’s immediate social connections. Within these networks, it is likely to identify relationships...

How do we sample uniformly at random from the unit dimensional simplex? It turns out there is an easy way to do it: generate i.i.d. uniform variables in [0,1] and let denote the k-th smallest among them. Then,   is a desired sample from the unit simplex . It is straight-forward to prove now the […]

As I bid farewell to Boston University, a place that has been my academic home over these past years, I am filled with a mix of emotions. The years since I started at BU and became a father have truly flown by. My tenure at BU, while challenging due to serious personal circumstances, has been […]

Jim Simons, the math genius who conquered Wall Street, died yesterday. Jim Simons was a renowned mathematician and hedge fund manager, widely recognized for founding Renaissance Technologies, one of the world’s most successful quantitative investment firms. With a background in mathematics, Simons contributed significantly to the field of geometry and...